In our copending application Ser. No. 06/348,608 filed Feb. 12, 1982, and assigned to the assignee of the present invention, there is described a pneumatic door closer wherein a piston rod extends through an elastomeric sleeve which is progressively compressed in an axial direction as the associated door is opened thereby to exert an increasing frictional braking force on the piston rod. The door closer of the present invention is an improvement over the earlier disclosed door closer in that it increases the braking action while the door is substantially open, say about sixty degrees or more, for better wind resistance and for preventing inadvertent slamming of the door into the fully open position. Moreover, the improved door closer of the present invention exerts a force which increasingly opposes swinging movement of the door as the door swings from the fully closed position toward the fully open position. The decreasing braking force results in a smooth, non-bounce return of the door from an open to a closed position.